Total energy non-conservation for explicit time dependent potentials

[brotherbobby]

Main Question or Discussion Point

I read from a book that the "total energy is not preserved when the potential depends explicitly on time", i.e. U(x,t). Can anyone show or prove it?

Many thanks.

 

[McLaren Rulez]

Total energy will be conserved. What happens is that you will be spending some energy in changing the potential U.

For instance, consider the potential energy of some test charge, T, placed near some charged particle, A. Of course the potential energy of T will change if you move particle A around. So, in that sense, the test charge's energy is changing. But anything you lose or gain will be covered by the energy used in moving particle A.